Question

The diagram shows a rhombus ABCD. The points B and D have coordinates (2, 10) and (6, 2) respectively, and A lies on the x-axis. The mid-point of BD is M. Find, by calculation, the coordinates of each of M, A and C

B (2, 10) D (6,2)

Answer 1

IR (2,10) "D (6,2) ABCD is a rhombus. The point B and I have wordinates (2,10) and (6,2) respectively, and A lies on the x-axis. M is the mid-point of BD. To find. The wordinates of (,) each of M, A and c. M is the mid-point of BD . The coordinates of M are (?+ • 10+2) 2) =(4,6) respectively (",",) and (12,/2). •Let A and c are the wordinates of A is on the xraxis • The diagonals of a rhombus bisect each other at a right : Mid-point of AC = Mid-point of BD = M. angle (^,the, I, th) =(4,6) [Mth 3 ) = (4.6) {: Y,=0 →nth 24, 2=6 => , +4=8. 2=12 AC + BD slope of Acx slope of BD = -1 2 x 2-1/2 = -1 ex-2=-1 =24 - - 9

adding equations and B. 22 = 32 ₂ = 32 = 16 Putting this value of n x+16=8 => = 8-16 >x, =-8 in B 2,228, ņ= 16, Y = 0, 2212 i. The coordinates of A are (-8,0) The coordinates of care (16,12) M=(4,6 A = (-8,0) (= (16,12)